Asymptotic expansions of multiple integrals of rapidly oscillating functions
Authors:
T. Iwaniec and A. Lutoborski
Journal:
Math. Comp. 50 (1988), 215228
MSC:
Primary 41A60
DOI:
https://doi.org/10.1090/S00255718198809178296
MathSciNet review:
917829
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Abstract: Expansions of multiple integrals \[ \int _{{a_1}}^{{b_1}} \cdots \int _{{a_n}}^{{b_n}} {w({\sigma _1}{x_1}, \ldots ,{\sigma _n}{x_n})g({x_1}, \ldots ,{x_n})\;d{x_1} \cdots d{x_n},} \] where w is a function on ${{\mathbf {R}}^n}$ which is $({b_k}  {a_k})$periodic in the kth variable, $k = 1, \ldots ,n$, and g is smooth, are given in terms of negative powers of the integers ${\sigma _1}, \ldots ,{\sigma _n}$. Estimates of the remainder term in the expansion are also given.

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© Copyright 1988
American Mathematical Society